Soft Tissue Biomechanics Research Articles

Biphasic finite element contact analysis of the knee joint using an augmented Lagrangian method

Biphasic contact analysis is essential to obtain a more complete understanding of soft tissue biomechanics; however, only a limited number of studies have addressed these types of problems. In this paper, a theoretically consistent biphasic finite element solution of the 2D axisymmetric human knee was developed, and an augmented Lagrangian method was used to enforce the biphasic continuity across the contact interface. The interaction between the fluid and solid matrices of the soft tissues of the knee joint, the stress and strain distributions within the meniscus, and the changes in stress and strain distributions in the articular cartilage of the femur and tibia after complete meniscectomy were investigated. It was found that (i) the fluid phase carries more than 60% of the load, which reinforces the need for the biphasic model for knee biomechanics; (ii) the inner third and outer two-thirds of the meniscus had different strain distributions; and (iii) the distributions of both maximum shear stress and maximum principal strain in articular cartilage changed after complete meniscectomy – with peak values increasing by over 350%.

Microscale Fiber Network Alignment Affects Macroscale Failure Behavior in Simulated Collagen Tissue Analogs

A tissue's microstructure determines its failure properties at larger length scales, however, the specific relationship between microstructure and macroscopic failure in native and engineered soft tissues (such as capsular ligaments, aortic aneurysms, or vascular grafts) has proven elusive. In this study, variations in the microscale fiber alignment in collagen gel tissue analogs were modeled in order to understand their effects on macroscale damage and failure outcomes. The study employed a multiscale finite-element (FE) model for damage and failure in collagen-based materials. The model relied on microstructural representative volume elements (RVEs) that consisted of stochastically-generated networks of discrete type-I collagen fibers. Fiber alignment was varied within RVEs and between layers of RVEs in a macroscopic FE model of a notched dogbone geometry. The macroscale stretch and the microscale response of fibers for each of the differently aligned cases were compared as the dogbone was uniaxially extended to failure. Networks with greater fiber alignment parallel to the direction of extension failed at smaller strains (with a 6-22% reduction in the Green strain at failure), however, at greater grip forces (a 28-60% increase) than networks with fibers aligned perpendicular to the extension. Alternating layers of crisscrossed network alignments (aligned ±45 deg to the direction of extension) failed at smaller strains but at greater grip forces than those created using one fiber alignment type. In summary, variations in microscale structure via fiber alignment produced different macroscale failure trends. To conclude, these findings may be significant in the realm of tissue engineering and in soft tissue biomechanics.

An augmented Lagrangian finite element formulation for 3D contact of biphasic tissues

Biphasic contact analysis is essential to obtain a complete understanding of soft tissue biomechanics, and the importance of physiological structure on the joint biomechanics has long been recognised; however, up to date, there are no successful developments of biphasic finite element contact analysis for three-dimensional (3D) geometries of physiological joints. The aim of this study was to develop a finite element formulation for biphasic contact of 3D physiological joints. The augmented Lagrangian method was used to enforce the continuity of contact traction and fluid pressure across the contact interface. The biphasic contact method was implemented in the commercial software COMSOL Multiphysics 4.2® (COMSOL, Inc., Burlington, MA). The accuracy of the implementation was verified using 3D biphasic contact problems, including indentation with a flat-ended indenter and contact of glenohumeral cartilage layers. The ability of the method to model multibody biphasic contact of physiological joints was proved by a 3D knee model. The 3D biphasic finite element contact method developed in this study can be used to study the biphasic behaviours of the physiological joints.

Medial patellofemoral ligament reconstruction - A novel technique.

Patellofemoral instability is initially treated conservatively and surgical treatment is reserved for resistant cases. Reconstruction of medial patellofemoral ligament has gained popularity these days as it attempts at restoring soft tissue anatomy and biomechanics of medial patellar restraint back to normal. Here we describe our novel transverse patella single tunnel and femoral interference screw technique to reconstruct the medial patellofemoral ligament using free autologous gracilis and semitendinosus grafts.

THE POISSON'S RATIO OF THE NUCLEUS PULPOSUS IS STRAIN DEPENDENT

Part of the Soft Tissue Biomechanics Session this presentation is to characterise the true Poisson’s ratio of the nucleus pulposus is strain dependent

A constrained von Mises distribution to describe fiber organization in thin soft tissues

The semi-circular von Mises distribution is widely used to describe the unimodal planar organization of fibers in thin soft tissues. However, it cannot accurately describe the isotropic subpopulation of fibers present in such tissues, and therefore an improved mathematical description is needed. We present a modified distribution, formed as a weighted mixture of the semi-circular uniform distribution and the semi-circular von Mises distribution. It is described by three parameters: β, which weights the contribution from each mixture component; k, the fiber concentration factor; and θ ( p ), the preferred fiber orientation. This distribution was used to fit data obtained by small-angle light scattering experiments from various thin soft tissues. Initial use showed that satisfactory fits of fiber distributions could be obtained (error generally < 1%), but at the cost of non-physically meaningful values of k and β. To address this issue, an empirical constraint between the parameters k and β was introduced, resulting in a constrained 2-parameter fiber distribution. Compared to the 3-parameter distribution, the constrained 2-parameter distribution fits experimental data well (error generally < 2%) and had the advantage of producing physically meaningful parameter values. In addition, the constrained 2-parameter approach was more robust to experimental noise. The constrained 2-parameter fiber distribution can replace the semi-circular von Mises distribution to describe unimodal planar organization of fibers in thin soft tissues. Inclusion of such a function in constitutive models for finite element simulations should provide better quantitative estimates of soft tissue biomechanics under normal and pathological conditions.

Finite extension and torsion of fiber-reinforced non-linearly elastic circular cylinders

In the context of the theory of non-linear elasticity for rubber-like materials, the problem of finite extension and torsion of a circular bar or tube has been widely investigated. More recently, this problem has attracted considerable attention in studies on the biomechanics of soft tissues and has been applied, for example, to examine the mechanical behavior of passive papillary muscles of the heart. A recent study in non-linear elasticity was concerned specifically with the effects of strain-stiffening on the response of solid circular cylinders in the combined deformation of torsion superimposed on axial extension. The cylinders are composed of incompressible isotropic non-linearly elastic materials that undergo severe strain-stiffening in the stress–stretch response. For two specific material models that reflect limiting chain extensibility at the molecular level, it was shown that, in the absence of an additional axial force, a transition value γ=γt of the axial stretch exists such that for γ<γt, the stretched cylinder tends to elongate on twisting whereas for γ>γt, the stretched cylinder tends to shorten on twisting. These results are in sharp contrast with those for classical models for rubber such as the Mooney–Rivlin (and neo-Hookean) models that predict that the stretched circular cylinder always tends to further elongate on twisting. Here we investigate similar issues for fiber-reinforced transversely isotropic circular cylinders. We consider a class of incompressible anisotropic materials with strain-energy densities that are of logarithmic form in the anisotropic invariant. These models reflect limited fiber extensibility and in the biomechanics context model the stretch induced strain-stiffening of collagen fibers on loading. They have been shown to model the mechanical behavior of fiber-reinforced rubber and many fibrous soft biological tissues. The consideration of anisotropy leads to a more elaborate mechanical response than was found for isotropic strain-stiffening materials. The results obtained here have important implications for extension–torsion tests for fiber-reinforced materials, for example in the development of accurate extension–torsion test protocols for determination of material properties of soft tissues.

Torsion of Incompressible Fiber-Reinforced Nonlinearly Elastic Circular Cylinders

Torsion of solid cylinders in the context of nonlinear elasticity theory has been widely investigated with application to the behavior of rubber-like materials. More recently, this problem has attracted attention in investigations of the biomechanics of soft tissues and has been applied, for example, to examine the mechanical behavior of passive papillary muscles of the heart. A recent study in nonlinear elasticity was concerned specifically with the effects of strain-stiffening on the torsional response of solid circular cylinders. The cylinders are composed of incompressible isotropic nonlinearly elastic materials that undergo severe strain-stiffening in the stress-stretch response. Here we investigate similar issues for fiber-reinforced transversely-isotropic circular cylinders. We consider a class of incompressible anisotropic materials with strain-energy densities that are of logarithmic form in the anisotropic invariant. These models reflect stretch induced strain-stiffening of collagen fibers on loading and have been shown to model the mechanical behavior of many fibrous soft biological tissues. The consideration of anisotropy leads to a more elaborate mechanical response than was found for isotropic strain-stiffening materials. The classic Poynting effect found for rubber-like materials where torsion induces elongation of the cylinder is shown to be significantly different for the transversely-isotropic materials considered here. For sufficiently large anisotropy and under certain conditions on the amount of twist, a reverse-Poynting effect is demonstrated where the cylinder tends to shorten on twisting The results obtained here have important implications for the development of accurate torsion test protocols for determination of material properties of soft tissues.

GPU-based real-time soft tissue deformation with cutting and haptic feedback

This article describes a series of contributions in the field of real-time simulation of soft tissue biomechanics. These contributions address various requirements for interactive simulation of complex surgical procedures. In particular, this article presents results in the areas of soft tissue deformation, contact modelling, simulation of cutting, and haptic rendering, which are all relevant to a variety of medical interventions. The contributions described in this article share a common underlying model of deformation and rely on GPU implementations to significantly improve computation times. This consistency in the modelling technique and computational approach ensures coherent results as well as efficient, robust and flexible solutions.

A new parameter identification method of soft biological tissue combining genetic algorithm with analytical optimization

The main goal of this paper is to provide simple parameter identification process for most of hyperelastic constitutive laws in biomechanics of soft tissues. The advantage of our approach lies on its rapidity and effectiveness, by reducing analytically the number of parameters to identify in the model during the identification procedure. With the use of genetic algorithms, the search for an adequate initial guess point is avoided and the space solution of the objective function is reduced to meet only parameters that cannot be calculated analytically. As an example, we focus on models that predict arterial wall behaviour such as laws based on Fung’s type energy function (Holzapfel, 2006) [14] and (Holzapfel et al., 2000 model) [15]. Our approach is applied on uniaxial extension tests and the results are compared with available data in the literature.

MECHANICAL ASPECTS OF A SINGLE-BUNDLE TIBIAL INTERFERENCE SCREW FIXATION IN A TENDON GRAFT ACL RECONSTRUCTION

Numerical methods applicable to the tibia bone and soft tissue biomechanics of an anterior cruciate ligament (ACL) reconstructed knee are presented in this paper. The aim is to achieve a better understanding of the mechanics of an ACL reconstructed knee. The paper describes the methodology applied in the development of an anatomically detailed three-dimensional ACL reconstructed knee model for finite element analysis from medical image data obtained from a computed tomography scan. Density segmentation techniques are used to geometrically define the knee bone structure and the encapsulated soft tissues configuration. Linear and nonlinear elastic constitutive material models are implemented to mechanically characterize the behavior of the biological materials. Preliminary numerical results for the model qualitative evaluation are presented.

Finite Element Algorithm for Frictionless Contact of Porous Permeable Media Under Finite Deformation and Sliding

This study formulates and implements a finite element contact algorithm for solid-fluid (biphasic) mixtures, accommodating both finite deformation and sliding. The finite element source code is made available to the general public. The algorithm uses a penalty method regularized with an augmented Lagrangian method to enforce the continuity of contact traction and normal component of fluid flux across the contact interface. The formulation addresses the need to automatically enforce free-draining conditions outside of the contact interface. The accuracy of the implementation is verified using contact problems, for which exact solutions are obtained by alternative analyses. Illustrations are also provided that demonstrate large deformations and sliding under configurations relevant to biomechanical applications such as articular contact. This study addresses an important computational need in the biomechanics of porous-permeable soft tissues. Placing the source code in the public domain provides a useful resource to the biomechanics community.

Dynamic properties of human tympanic membrane &amp;ndash; experimental measurement and modelling analysis

An experimental setup for dynamic testing of human tympanic membrane (TM) with the material testing system and laser Doppler vibrometry is reported in this paper. The experiment on TM specimen was simulated in finite element (FE) model using acoustic-structure coupled analysis. The generalised standard linear solid (Weichert) model was used as the constitutive law for the TM, and the dynamic properties of the TM was derived by inverse-problem solving method. The complex modulus in frequency-domain and the relaxation modulus in time-domain were obtained. The mean value of storage modulus of eight TM specimens was 54.34 at the frequency of 200 Hz and 65.54 MPa at 8,000 Hz, while the mean loss modulus was 1.92 at 200 Hz and 6.12 MPa at 8,000 Hz. These results were compared with the published data measured with the miniature split Hopkinson tension bar. The methods and data reported here contribute to the field of soft tissue biomechanics in both experimental measurement and theoretical analysis of ear.

Biomechanical and histological characteristics of passive esophagus: Experimental investigation and comparative constitutive modeling

Information on the passive biomechanical properties of two-layered esophagus is still limited, although this would enhance our understanding of its physiology/pathophysiology and help to address problems in surgery, medical-device applications, and for the optimal design of prostheses. In this study, rabbit esophagi were excised and dissected into mucosa–submucosa and muscle layers that were submitted to histological quantification of elastin and collagen content and orientation, as well as to inflation-extension testing and geometrical analysis, i.e. delineation of the zero-stress state serving as a reference configuration for biomechanical analysis. The pressure–radius data of both layers displayed a monotonically rising slope with inflating pressure, unlike the sigma shape characterizing elastin-rich tissues, for which biphasic constitutive models were initially postulated. Three phenomenological expressions of strain-energy function (SEF), commonly appearing in soft-tissue biomechanics literature, were used in an attempt to model the pseudoelastic response of esophageal tissue, namely the exponential Fung-type SEF, and the combined neo-Hookean (isotropic) or quadratic (anisotropic) and exponential Fung-type SEF. Accurate fits were attained for the pressure–radius–force data, spanning a wide range of longitudinal stretch ratios, when using the exponential form; the biphasic SEFs failed to generate improved fits, being also over-parameterized. According to the calculated material parameters, mucosa–submucosa was stiffer than muscle in both directions, justified by our histological observation of increased collagen content in that layer, and tissue was stiffer longitudinally, substantiated by the increased elastin and collagen contents and their preferential alignment towards that direction. Our results demonstrate that the passive response of esophagus is best modeled with an exponential Fung-type SEF.

The stress relaxation characteristics of composite matrices etched to produce nanoscale surface features

Many synthetic and xenogenic natural matrices have been explored in tissue regeneration, however, they lack either mechanical strength or cell colonization characteristics found in natural tissue. Moreover natural matrices such as small intestinal submucosa (SIS) lack sample to sample homogeneity, leading to unpredictable clinical outcomes. This work explored a novel fabrication technique by blending together the useful characteristics of synthetic and natural polymers to form a composite structure by using a NaOH etching process that produces nanoscale surface features. The composite scaffold was formed by sandwiching a thin layer of PLGA between porous layers of gelatin–chitosan. The etching process increased the surface roughness of PLGA membrane, allowing easy spreading of the hydrophilic gelatin–chitosan solution on its hydrophobic surface and reducing the scaffold thickness by nearly 50% than otherwise. The viscoelastic properties of the scaffold, an area of mechanical analysis which remains largely unexplored in tissue regeneration was assessed. Stress relaxation experiments of the “ramp and hold” type performed at variable ranges of temperature (25 °C and 37 °C), loading rates (3.125% s −1 and 12.5% s −1) and relaxation times (60 s, 100 s and 200 s) found stress relaxation to be sensitive to temperature and the loading rate but less dependent on the relaxation time. Stress relaxation behavior of the composite matrix was compared with SIS structures at 25 °C (hydrated), 3.125% s −1 loading rate and 100 s relaxation time which showed that the synthetic matrix was found to be strain softening as compared to the strain hardening behavior exhibited by SIS. Popularly used quasi-linear viscoelastic (QLV) model to describe biomechanics of soft tissues was utilized. The QLV model predicted the loading behavior with an average error of 3%. The parameters of the QLV model predicted using nonlinear regression analysis appear to be in concurrence with soft tissues.

Fung's model of arterial wall enhanced with a failure description.

One of the seminal contributions of Y.C. Fung to biomechanics of soft tissue is the introduction of the models of arterial deformation based on the exponential stored energy functions, which are successfully used in various applications. The Fung energy functions, however, explain behavior of intact arteries and do not include a description of arterial failure. The latter is done in the present work where Fung's model is enhanced with a failure description. The description is based on the introduction of a limiter for the stored energy - the average energy of chemical bonds, which can be interpreted as a failure constant characterizing the material 'toughness'. The limiting failure energy controls materials softening, which indicates the onset of failure. We demonstrate the efficiency of the enhanced Fung formulation on a problem of the arterial inflation under internal pressure. We show, particularly, that residual stresses delay the onset of failure. The considered softening hyperelasticity approach is an alternative to the simplistic pointwise failure criteria of strength of materials on the one hand and the sophisticated approach of damage mechanics involving internal variables on the other hand.

Computational Biomechanics for Medicine III - Workshop proceedings

A novel partnership between surgeons and machines, made possible by advances in computing and engineering technology, could overcome many of the limitations of traditional surgery. By extending surgeons’ ability to plan and carry out surgical interventions more accurately and with less trauma, Computer-Integrated Surgery (CIS) systems could help to improve clinical outcomes and the efficiency of health care delivery. CIS systems could have a similar impact on surgery to that long since realized in Computer-Integrated Manufacturing (CIM). Mathematical modeling and computer simulation have proved tremendously successful in engineering. Computational mechanics has enabled technological developments in virtually every area of our lives. One of the greatest challenges for mechanists is to extend the success of computational mechanics to fields outside traditional engineering, in particular to biology, the biomedical sciences, and medicine.Computational Biomechanics for Medicine Workshop series was established in 2006 with the first meeting held in Copenhagen. The third workshop was held in conjunction with the Medical Image Computing and Computer Assisted Intervention Conference (MICCAI 2008) in New York on 10 September 2008. It provided an opportunity for specialists in computational sciences to present and exchange opinions on the possibilities of applying their techniques to computer-integrated medicine.Computational Biomechanics for Medicine III was organized into two streams: Computational Biomechanics of Soft Tissues, and Computational Biomechanics of Tissues of Musculoskeletal System. The application of advanced computational methods to the following areas was discussed: - Medical image analysis; - Image-guided surgery; - Surgical simulation; - Surgical intervention planning; - Disease prognosis and diagnosis; - Injury mechanism analysis; - Implant and prostheses design; - Medical robotics.After rigorous review of full (eight-to-twelve page) manuscripts we accepted 15 papers, collected in this volume. They were split equally between podium and poster presentations. The proceedings also include abstracts of two invited lectures by world-leading researchers Professor Chwee Teck Lim from national University of Singapore and Dr. David Lloyd from The University of Western Australia.Information about Computational Biomechanics for Medicine Workshops, including Proceedings of previous meetings is available at http://cbm.mech.uwa.edu.au/ .We would like to thank the MICCAI 2008 organizers for help with administering the Workshop, invited lecturers for deep insights into their research fields, the authors for submitting high quality work, and the reviewers for helping with paper selection.

Inhomogeneous shearing of strain-stiffening rubber-like hollow circular cylinders

The purpose of this paper is to investigate the effects of strain-stiffening for the classical problems of axial and azimuthal shearing of a hollow circular cylinder composed of an incompressible isotropic non-linearly elastic material. For some specific strain-energy densities that give rise to strain-stiffening in the stress–stretch response, the stresses and resultant axial forces are obtained in explicit closed form. While such results are well known for classical constitutive models such as the Mooney–Rivlin and neo-Hookean models, our main focus is on materials that undergo severe strain-stiffening in the stress–stretch response. In particular, we consider in detail two phenomenological constitutive models that reflect limiting chain extensibility at the molecular level and involve constraints on the deformation. The amount of shearing that tubes composed of such materials can sustain is limited by the constraint. Numerical results are also obtained for an exponential strain-energy that exhibits a less abrupt strain-stiffening effect. Potential applications of the results to the biomechanics of soft tissues are indicated.

TH‐B‐351‐01: Elastography — Real‐Time Ultrasound Elasticity Imaging Technique

Ultrasound elasticity imaging or elastography is real‐time imaging technique capable of determining tissue elasticity of certain organs such as breast and prostate. Elasticity imaging, applied during standard ultrasound examinations, is a patient‐friendly, reliable and cost‐efficient method to diagnose cancer or other diseases based on the changes in tissue elasticity that are usually related to some abnormal, pathological processes.The main objective of this course is to expose the audience to elasticity imaging with emphasis to principles, approaches and applications. The course will provide both a broad overview and comprehensive understanding of both static and dynamic approaches in elasticity imaging. Starting with a brief historical introduction to elasticity imaging, we will examine the foundation and basic principles of elasticity imaging (theory of elasticity including both the equation of equilibrium and the wave equation, mechanical properties of soft tissues, etc.). We will then discuss practical aspects of ultrasound elasticity imaging including imaging hardware, signal and image processing algorithms, etc. Motion tracking methods will be introduced and analyzed. In this part of the course, we will also analyze noise (sources) and primary artifacts. Finally, elasticity imaging techniques and their clinical applications will be presented. The course will conclude with overview of several experimental and commercial systems capable of elasticity imaging.Educational Objectives:1. Understand the underlying principles of both static and dynamic approaches in elasticity imaging.2. Understand the practical aspects related to an elasticity imaging experiment including design, data acquisition and signal/image processing.3. Understand the issues related to clinical application of ultrasound elasticity imaging.Stanislav Emelianov received the B.S. and M.S. degrees in physics and acoustics in 1986 and 1989, respectively, from the Moscow State University, and the Ph.D. degree in physics in 1993 from Moscow State University, and the Institute of Mathematical Problems of Biology of the Russian Academy of Sciences, Russia. In 1989, he joined the Institute of Mathematical Problems of Biology, where he was engaged in both mathematical modeling of soft tissue biomechanics and experimental studies of noninvasive visualization of tissue mechanical properties. Following his graduate work, he moved to the University of Michigan, Ann Arbor, as a post‐Doctoral Fellow in the Bioengineering Program, and Electrical Engineering and Computer Science Department. From 1996 to 2002, Dr. Emelianov was a Research Scientist at the Biomedical Ultrasonics Laboratory at the University of Michigan. During his tenure at Michigan, Dr. Emelianov was involved primarily in the theoretical and practical aspects of elasticity imaging. Dr. Emelianov is currently an Associate Professor of Biomedical Engineering at the University of Texas at Austin. His research interests are in the areas of medical imaging for therapeutics and diagnostic applications, elasticity imaging, ultrasound microscopy, photoacoustic imaging, cellular/molecular imaging, and functional imaging.

On planar biaxial tests for anisotropic nonlinearly elastic solids. A continuum mechanical framework

The mechanical testing of anisotropic nonlinearly elastic solids is a topic of considerable and increasing interest. The results of such testing are important, in particular, for the characterization of the material properties and the development of constitutive laws that can be used for predictive purposes. However, the literature on this topic in the context of soft tissue biomechanics, in particular, includes some papers that are misleading since they contain errors and false statements. Claims that planar biaxial testing can fully characterize the three-dimensional anisotropic elastic properties of soft tissues are incorrect. There is therefore a need to clarify the extent to which biaxial testing can be used for determining the elastic properties of these materials. In this paper this is explained on the basis of the equations of finite deformation transversely isotropic elasticity, and general planar anisotropic elasticity. It is shown that it is theoretically impossible to fully characterize the properties of anisotropic elastic materials using such tests unless some assumption is made that enables a suitable subclass of models to be preselected. Moreover, it is shown that certain assumptions underlying the analysis of planar biaxial tests are inconsistent with the classical linear theory of orthotropic elasticity. Possible sets of independent tests required for full material characterization are then enumerated.